The proof of this lemma can be found in [1]}. Combine Lemma REF , REF , REF  with Equation (REF ), we obtain that:
\(\mathbb {E}\sum _{k=1}^{N}\Vert g_{k-1}\Vert _{S_{k-1}^{-1}}^2 \leqslant \frac{4}{\eta ^2}\cdot 2dD^2\delta N^{\alpha } + 24\cdot \left(\frac{\delta \sigma ^2}{m}+4d\delta \cdot N^{\alpha }\right) + 10\cdot \frac{2dG^2\cdot N^{\alpha }}{\delta }.\) 
